On interrelations between trivial and nontrivial basic sets of structurally stable diffeomorphisms of surfaces
The article is devoted to interrelations between an existence of trivial and nontrivial basic sets of A-diffeomorphisms of surfaces. We prove that if all trivial basic sets of a structurally stable diffeomorphism of surface $M^2$ are source periodic points $\alpha_1, …, \alpha_k$, then the non-wandering set of this diffeomorphism consists of points $\alpha_1, …, \alpha_k$ and exactly one one-dimensional attractor $\Lambda$. We give some sufficient conditions for attractor $\Lambda$ to be widely situated. Also, we prove that if a non-wandering set of a structurally stable diffeomorphism contains a nontrivial zero-dimensional basic set, then it also contains source and sink periodic points.